The Quality of service (QoS) routing has been receiving increasingly intensive attention in the mobile ad hoc networks (MANETs) fields, but it is difficult to solve the problem for the nature of MANETs such as performance constraints and dynamic network topology. In order to increase the probability of success in finding QoS feasible paths and reduce average cost in flooding path discovery scheme of the traditional MANETs routing protocols, we proposed a heuristic and distributed route discovery method named RLGAMAN that supports QoS requirement for MANETs in this paper. This method integrates the route discovery scheme with a reinforcement learning (RL) method that only utilizes the local information for the dynamic network environment; and the route expand scheme based on genetic algorithms (GA) method to avoid the problem of stagnation route. We investigate the performance of the RLGAMAN by simulation experiment bed in NS2. Compared with the traditional method, the experiment results showed the network performance is improved obviously, and RLGAMAN is efficient and effective.